Euler's Pentagonal Number Theorem and the Rogers-Fine Identity

George E. Andrews, Jordan Bell

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Euler discovered the pentagonal number theorem in 1740 but was not able to prove it until 1750. He sent the proof to Goldbach and published it in a paper that finally appeared in 1760. Moreover, Euler formulated another proof of the pentagonal number theorem in his notebooks around 1750. Euler did not publish this proof or communicate it to his correspondents, probably because of the difficulty of clearly presenting it with the notation at the time. In this paper we show that the method of Euler's unpublished proof can be used to give a new proof of the celebrated Rogers-Fine identity.

Original languageEnglish (US)
Pages (from-to)411-420
Number of pages10
JournalAnnals of Combinatorics
Issue number3
StatePublished - Aug 2012

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics


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